Mathematical Modeling in Modelica: The Art of Compressing Reality

Kurzfassung

When we enjoy the freedom of mathematical expression in Modelica, we build on the legacy of many great scientist who condensed the laws of nature into elegant equations. This makes differential-algebraic equations an extremely powerful modeling tool to compress the real system down to an intelligible, computable and hopefully controllable form. But all too often, this compression is flawed and as simulation engineers we run into errors. For large modeling efforts, the freedom of expression needs to be rigorously constrained by a clear methodology. All experienced modelers know that the dull application of text-book equations will not bode well in a large, challenging simulation project. But how to do better? How to ensure that you reach a computational feasible form that is still effective? How to ensure that what works on component level will work on system level? In this keynote, I revisit the principles of idealization that modelers often apply without being aware of them. I demonstrate how quickly idealization can lure you into problems rather than solving them. But better understanding the process of idealization also offers an approach leading to a robustly solvable form, even for large complex systems. The immediate practical value is demonstrated by the simulation of complex thermal architectures and the real-time simulation of stiff mechanical contact problems.